Answer
$\dfrac {1\pm \sqrt {85}}{6}$
Work Step by Step
$\log _{5}\left( 3x+2\right) +\log _{5}\left( x-1\right) =1\Rightarrow \log _{5}\left( \left( 3x+2\right) \left( x-1\right) \right) =\log _{5}5$
$\left( 3x+2\right) \left( x-1\right) =5\Rightarrow 3x^{2}-x-2=5\Rightarrow 3x^{2}-x-7=0$
$x_{1,2}=\dfrac {-b\pm \sqrt {b^{2}-4ac}}{2a}=\dfrac {1\pm \sqrt {1-4\times 3\times \left( -7\right) }}{2\times 3}=\dfrac {1\pm \sqrt {85}}{6}$
